A New TV-Stokes Model with Augmented Lagrangian Method for Image Denoising and Deconvolution

Recently, TV-Stokes model has been widely researched for various image processing tasks such as denoising and inpainting. In this paper, we introduce a new TV-Stokes model for image deconvolution, and propose fast and efficient iterative algorithms based on the augmented Lagrangian method. The new TV-Stokes model is a two-step model: in the first step, a smoothed and divergence free tangential field of the observed image is recovered based on total variation (TV) minimization and a new data fidelity term; in the second step, the image is reconstructed by minimizing the distance between the unit image gradient and the regularized unit normal direction. Numerical experiments demonstrate that the proposed model has the potential to outperform popular TV-based restoration methods in preserving texture details and fine structures. As a result, an improvement in signal-to-noise ratio (SNR) is obtained for deconvolution and denoising results.